I'm having trouble getting mathematica to compute complex conjugates
of some fairly simple expressions:
If I type the following:
$Assumptions = {g \[Element] Reals, f \[Element] Reals}
u1 = f + \[ImaginaryI] g
u2 = f - \[ImaginaryI] g
Then the command:
Refine[Conjugate [c1 u1]]
returns:
f - \[ImaginaryI] g) Conjugate[c1]
and the command:
Refine[Conjugate[c1 u1 + u2]]
returns:
f + \[ImaginaryI] g + (f - \[ImaginaryI] g) Conjugate[c1]
as I would expect. But the command:
Refine[Conjugate[c1 u1 + c2 u2]]
returns:
Conjugate[c2 (f - \[ImaginaryI] g) + c1 (f + \[ImaginaryI] g)]
i.e. it refuses to distribute the complex conjugate throughout the
expression. What I would like it to tell me is:
(f + \[ImaginaryI] g) Conjugate[c2] + (f - \[ImaginaryI] g)
Conjugate[c1]
The closest I have been able to come to getting what I want is by
using:
ComplexExpand[Refine[Conjugate[ c1 u1 + c2 u2]], {c1, c2}]
but this separates c1 and c2 into their real and imaginary parts. The
above expressions are much simpler than the ones I REALLY want
Mathematica's help in simplifying. If I use this ComplexExpand
command, then I'm going to have to recombine them into complex numbers
again, which would be very very bad.
Thanks,
Roy